%0 Generic %1 dong2021attention %A Dong, Yihe %A Cordonnier, Jean-Baptiste %A Loukas, Andreas %D 2021 %K 2021 attention deep-learning %T Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth %U http://arxiv.org/abs/2103.03404 %X Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.

@misc{dong2021attention, abstract = {Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.}, added-at = {2021-03-30T21:49:03.000+0200}, author = {Dong, Yihe and Cordonnier, Jean-Baptiste and Loukas, Andreas}, biburl = {https://www.bibsonomy.org/bibtex/2f61b5deb0ecc01f257f92f546e34d227/analyst}, description = {[2103.03404] Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth}, interhash = {5aee65ee5572bb5580c1ebbf247234aa}, intrahash = {f61b5deb0ecc01f257f92f546e34d227}, keywords = {2021 attention deep-learning}, note = {cite arxiv:2103.03404}, timestamp = {2021-03-30T21:49:03.000+0200}, title = {Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth}, url = {http://arxiv.org/abs/2103.03404}, year = 2021 }